On the jump classes of noncuppable enumeration degrees

We prove that for every Σ0 2 enumeration degree b there exists a noncuppable Σ0 2 degree a > 0e such that b ≤e a and a ≤e b . This allows us to deduce, from results on the high/low jump hierarchy in the local Turing degrees and the jump preserving properties of the standard embedding ι : DT → De, that there exist Σ0 2 noncuppable enumeration degrees at every possible—i.e. above low1—level of the high/low jump hierarchy in the context of De.

• Type: Journal
• Year: 2011
• Where: JSYML
• Authors: Charles M. Harris
• Keywords: Enumeration Degrees, JSYML 2011, Jump Hierarchy, Local Turing Degrees